print( """
\tWelcome to the Babylonian Method
This program will generate five steps of Heron's method for
a number S that you will have to enter. Heron's method generates
better and better approximations for the square root of S.
""")
S = float(input('Please input the value of S: '))

appr = S/2
appr = 0.5*(appr + S/appr)
print('My guess now is', appr)
appr = 0.5*(appr + S/appr)
print('My guess now is', appr)
appr = 0.5*(appr + S/appr)
print('My guess now is', appr)
appr = 0.5*(appr + S/appr)
print('My guess now is', appr)
appr = 0.5*(appr + S/appr)
print('My final guess is', appr)
error = abs(S**0.5-appr)/S**0.5
print('The error is ', error*100,'%')